Random Sorting Networks

A sorting network is a shortest path from 12...n to n...21 in the Cayley graph of S_n generated by nearest-neighbour swaps. We prove that for a uniform random sorting network, as n->infinity the space-time process of swaps converges to the product of semicircle law and Lebesgue measure. We conjecture that the trajectories of individual particles converge to random sine curves, while the permutation matrix at half-time converges to the projected surface measure of the 2-sphere. We prove that, in the limit, the trajectories are Holder-1/2 continuous, while the support of the permutation matrix lies within a certain octagon. A key tool is a connection with random Young tableaux.Comment: 38 pages, 12 figure

Tardive syndromes

Dopamine receptor-blocking antipsychotics, first introduced into clinical practice in 1952, were hailed as a panacea in the treatment of a number of psychiatric disorders. However, within 5 years, this notion was to be shattered by the recognition of both acute and chronic drug-induced movement disorders which can accompany their administration. Tardive syndromes, denoting the delayed onset of movement disorders following administration of dopamine receptor-blocking (and also other) drugs, have diverse manifestations ranging from the classic oro-bucco-lingual dyskinesia, through dystonic craniocervical and trunk posturing, to abnormal breathing patterns. Although tardive syndromes have been an important part of movement disorder clinical practice for over 60 years, their pathophysiologic basis remains poorly understood and the optimal treatment approach remains unclear. This review summarises the current knowledge relating to these syndromes and provides clinicians with pragmatic, clinically focused guidance to their management

Isoscalar meson spectroscopy from lattice QCD

We extract to high statistical precision an excited spectrum of single-particle isoscalar mesons using lattice QCD, including states of high spin and, for the first time, light exotic JPC isoscalars. The use of a novel quark field construction has enabled us to overcome the long-standing challenge of efficiently including quark-annihilation contributions. Hidden-flavor mixing angles are extracted and while most states are found to be close to ideally flavor mixed, there are examples of large mixing in the pseudoscalar and axial sectors in line with experiment. The exotic JPC isoscalar states appear at a mass scale comparable to the exotic isovector states.Comment: 4 pages, 4 figure

Invariance Principle for the Random Lorentz Gas -- Beyond the Boltzmann-Grad Limit

We prove the invariance principle for a \emph{random Lorentz-gas} particle in 3 dimensions under the Boltzmann-Grad limit and simultaneous diffusive scaling. That is, for the trajectory of a point-like particle moving among infinite-mass, hard-core, spherical scatterers of radius r, placed according to a Poisson point process of density ϱ, in the limit ϱ→∞, r→0, ϱr2→1 up to time scales of order T=o(r−2|logr|−2). To our knowledge this represents the first significant progress towards solving rigorously this problem in classical nonequilibrium statistical physics, since the groundbreaking work of Gallavotti (1969), Spohn (1978) and Boldrighini-Bunimovich-Sinai (1983). The novelty is that the diffusive scaling of particle trajectory and the kinetic (Boltzmann-Grad) limit are taken simultaneously. The main ingredients are a coupling of the mechanical trajectory with the Markovian random flight process, and probabilistic and geometric controls on the efficiency of this coupling. Similar results have been earlier obtained for the weak coupling limit of classical and quantum random Lorentz gas, by Komorowski-Ryzhik (2006), respectively, Erd\H os-Salmhofer-Yau (2007). However, the following are substantial differences between our work and these ones: (1) The physical setting is different: low density rather than weak coupling. (2)The method of approach is different: probabilistic coupling rather than analytic/perturbative. (3) Due to (2), the time scale of validity of our diffusive approximation -- expressed in terms of the kinetic time scale -- is much longer and fully explicit

Benign tremulous parkinsonism of the young-consider Parkin

Benign tremulous parkinsonism is generally considered a disease of the elderly, characterised by dominance of tremor over other motor manifestations, and by slower disease progression. Herein, we draw attention to a different clinical syndrome, benign tremulous parkinsonism of the young, which we have observed in Parkin disease

Movement disorders in systemic autoimmune diseases: Clinical spectrum, ancillary investigations, pathophysiological considerations

With the advances in neuroimmunology especially due to the discovery of new neuronal antibodies, the recognition of treatable antibody-related movement disorders has recently received much attention. In contrast, the identification and characterisation of movement disorders associated with systemic autoimmune diseases remains a substantially unexplored area. Beyond the classic few associations such as chorea and antiphospholipid syndrome, or ataxia and coeliac disease, movement disorders have been reported in association with several systemic autoimmune diseases, however a clear image of clinical phenotypes, investigations, and treatment outcomes in these conditions has never been drawn. In this review, we analyse data from approximately 300 cases and summarise the epidemiological, clinical and diagnostic features of movement disorders associated with systemic autoimmune diseases, and the available knowledge about treatment and outcomes. We highlight that movement disorders in systemic autoimmune conditions are frequently the only or among a few presenting manifestations and are mostly treatable disorders responding to immunotherapy or dietary modifications. We point out the pertinent combination of clinical features and investigations which can suggest the underlying autoimmune nature of these movement disorders, and thus address the most appropriate treatment